The observation of the emergent properties of the patterns in the systems can be done mathematically using traditional central limit theorem by calculating large number of outcomes perceived from hidden processes of the distribution of the interacting random variables \(\lbrace x_i\rbrace ;i=1,2,...,N\)  corresponding to the aggregated \(N\)  components of the pattern [1]}, [2]}, [3]}. Depending on the observed properties of the probability distribution, the pattern can be in one of the classical patterns, namely, Norma, Poisson, Power law patterns etc [4]} and these patterns, in most of the biological systems, are dynamic in nature depending on the fluctuations driving them and limiting distribution conditions [5]}. If the spatiotemporal events are scattered randomly throughout the system, the probability distribution function becomes Poisson distribution and the pattern corresponds to classical Poisson pattern [2]}, [3]}, [4]}. Since Poisson pattern is generally generated from the random processes smaller-scales, the basin of attraction of such patterns have aggregation of large scale small-scale random processes by segregating from nonrandom processes [9]}. On the other hand, classical Normal pattern stores the information of mean \(\langle x\rangle \)  and variance \(\sigma ^2\)  in the aggregation process of the components in the pattern \(\mathcal {P}[\langle x\rangle ,\sigma ^2]\) , where, sum of the uncorrelated small-scaled fluctuations of the components during the aggregation process cancels out to attract towards a certain form of spatiotemporal regular aggregated pattern [1]}, [4]}. Hence, the dynamics of the aggregated components in such classical Normal patterns follow Brownian motion [12]}. Further, if the aggregated pattern keeps only the information of mean, the pattern falls in exponential pattern \(\displaystyle \mathcal {P}[x]=\frac{1}{\langle x\rangle }e^{-\frac{x}{\langle x\rangle }}\) , where, the pattern is contributed from the waiting time characterization of random events and the distribution has memoryless property [4]}. If the aggregation pattern preserves the information of geometric mean, the pattern follows classical Power law pattern which can have fractal patterns which have self-similar process \(\displaystyle \frac{\mathcal {P}[\alpha x]}{\mathcal {P}[x]}=\alpha ^h=F(\alpha )\) , where, \(h\)  is self-similarity exponent [14]}, [15]}. From these probability distribution functions, one can measure hidden information stored in the respective patterns by calculating Shannon entropy, \(\displaystyle \mathcal {H}=-\sum _{i}\mathcal {P}_i[x]ln\mathcal {P}_i[x]\)  [16]}.
